3x^0/y+2y^-1-y^-3/y^-2 eching

$$\frac { 3 x ^ { 0 } } { y } + 2 y ^ { - 1 } - \frac { y ^ { - 3 } } { y ^ { - 2 } }$$

Baholash

$$\frac{4}{y}$$

Qisqa yechim qadamlari

y^{-2} ni y^{-3}y sifatida qaytadan yozish. Surat va maxrajdagi ikkala y^{-3} ni qisqartiring.

$$\frac{3x^{0}}{y}+2y^{-1}-\frac{1}{y}$$

0 daraja ko‘rsatkichini x ga hisoblang va 1 ni qiymatni oling.

$$\frac{3\times 1}{y}+2y^{-1}-\frac{1}{y}$$

3 hosil qilish uchun 3 va 1 ni ko'paytirish.

$$\frac{3}{y}+2y^{-1}-\frac{1}{y}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2y^{-1} ni \frac{y}{y} marotabaga ko'paytirish.

$$\frac{3}{y}+\frac{2y^{-1}y}{y}-\frac{1}{y}$$

\frac{3}{y} va \frac{2y^{-1}y}{y} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3+2y^{-1}y}{y}-\frac{1}{y}$$

3+2y^{-1}y ichidagi ko‘paytirishlarni bajaring.

$$\frac{3+2}{y}-\frac{1}{y}$$

3+2 hisob-kitobini qiling.

$$\frac{5}{y}-\frac{1}{y}$$

\frac{5}{y} va \frac{1}{y} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring. 4 olish uchun 5 dan 1 ni ayirish.

$$\frac{4}{y}$$

y ga nisbatan hosilani topish

$$-\frac{4}{y^{2}}$$

Derivativ ifodasidan foydalanish qadamlari

y^{-2} ni y^{-3}y sifatida qaytadan yozish. Surat va maxrajdagi ikkala y^{-3} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3x^{0}}{y}+2y^{-1}-\frac{1}{y})$$

0 daraja ko‘rsatkichini x ga hisoblang va 1 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3\times 1}{y}+2y^{-1}-\frac{1}{y})$$

3 hosil qilish uchun 3 va 1 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3}{y}+2y^{-1}-\frac{1}{y})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2y^{-1} ni \frac{y}{y} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3}{y}+\frac{2y^{-1}y}{y}-\frac{1}{y})$$

\frac{3}{y} va \frac{2y^{-1}y}{y} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3+2y^{-1}y}{y}-\frac{1}{y})$$

3+2y^{-1}y ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3+2}{y}-\frac{1}{y})$$

3+2 hisob-kitobini qiling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{5}{y}-\frac{1}{y})$$

\frac{5}{y} va \frac{1}{y} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring. 4 olish uchun 5 dan 1 ni ayirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{4}{y})$$

ax^{n} hosilasi – nax^{n-1}.

$$-4y^{-1-1}$$

-1 dan 1 ni ayirish.

$$-4y^{-2}$$